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There were 30 sales of homes worth £1million or more between August and October - up from 14 in the previous three months.

The market for luxury homes stalled earlier this year following the introduction of the Scottish Government's Land and Buildings Transaction Tax.

The levy, which replaced stamp duty, meant that those buying expensive properties had to pay more tax than they would have previously.

Christine Campbell, Your Move managing director in Scotland, said: "Average property prices in Scotland have shot up £1,600 in October, twice the £761 rise witnessed in the month of September, as sales of million-pound home start to glow again."

She added: "This smouldering growth means that we have seen the largest month-on-month rise in property values since the introduction of the Land and Buildings Transaction Tax in April this year and the fourth biggest monthly jump since the August 2007, at the height of the housing boom.

"On an annual basis, house price growth is also shining brightly, up by 1.6%, the largest increase in five months."

Meanwhile, in a separate report, the Council of Mortgage Lenders (CML) yesterday revealed that house purchase lending soared by eight per cent in October.

First-time buyers across the UK borrowed £4.6billion in a total of 29,900 loans - up 8% month-on-month and 3% year-on-year.

Home movers took out 35,400 loans, up 9% month-on-month and 3% compared to October 2014. In total, this was £7.1billion borrowed, up 8% on September and 13% year-on-year.

Paul Smee, director general of the CML, said: "Homeowner and buy-to-let activity have both continued the upward trend seen last month.

"The market looks set to finish the year strong, despite taking time to gain momentum after a slow start to 2015.

"With increasing employment and the current absence of inflationary pressures in the UK, conditions for continuing demand in the housing market seem likely going into the new year. How supply will respond to this challenge going forward is a crucial question for 2016."